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Abstract

Accelerating beams are wave packets that preserve their shape while propagating along curved trajectories. Their unique characteristics have opened the door to applications that range from optical micromanipulation and plasma-channel generation to laser micromachining. Here, we demonstrate, theoretically and experimentally, that accelerating beams can be generated with a variety of arbitrarily chosen transverse shapes. We present a general method to construct such beams in the paraxial and nonparaxial regime and demonstrate experimentally their propagation in the paraxial case. The key ingredient of our method is the use of the spectral representation of the accelerating beams, which offers a unique and compact description of these beams. The on-demand accelerating light patterns described here are likely to give rise to new applications and add versatility to the current ones.

Figures (5)

Accelerating beams with on-demand transverse shapes: (a) triangle, (b) cosine-Gauss and (c) triangle+i cosine-Gauss. First row, desired target modulation Y (v), blue/red line are the real/imaginary parts and the black line is the vertical y-line profile of the beam at the local maxima of the horizontal x-modulation. Second row, line spectrum of the desired beam. Third row, intensity of the engineered accelerating beams. Last row, propagation of the accelerating beams with no apodization, exponential apodization and Gaussian apodization.

The behavior of our method to shape accelerating beams as a function of the extent of the spectrum of the desired modulation Y (y/α), for (a) Mexican hat and (b) random function modulation. The red line is the desired target modulation; the blue lines are the beam y-line profile at different local x-maxima of the beam invariant structure. The darkest tone of blue stands for the first x-maximum. Each row represents a different extent of the desired modulation.

Experimental realization of accelerating beams with on-demand transverse structures. The first row depicts the simulated optical intensity distributions of accelerating beams with different transverse patterns; the blue line shows the desired y-modulation. The second to fifth row show the experimental intensity distribution propagation of the generated beams at z =0, 15, 30 and 45 cm. Each rectangle depicts a 3.46 cm × 4.76 cm portion of the image. The last column shows an Airy beam for comparison.